Bridging the Gap between Structural and Statistical Pattern Recognition Horst Bunke Melchor Visiting Professor Department of Computer Science and Engineering University of Notre Dame and Institute of Computer Science and Applied Mathematics University of Bern, Switzerland bunke@iam.unibe.ch http://www.iam.unibe.ch/fki/staff/prof.-dr.-horst-bunke
Contents – Introduction – Graph Kernels and Graph Embedding – Automatic Transcription of Handwritten Medieval Texts – Brain State Decoding using fMRI – Summary, Discussion, and Conclusions
Introduction Traditional subdivision of pattern recognition:
Introduction Traditional subdivision of pattern recognition:
Statistical Approach
Structural Approach
• Overview • Overcoming the limitations: – Graph kernels – Graph embedding
Illustration of a problem that becomes linearly separable after transformation into a new feature space:
Illustration: Random Walk Kernel
Graph Embedding • Previous work: Fingerprints in chemo-informatics, graphlets Topological features from complex network research Various features based on eigen-decomposition, Ihara coefficients, etc.
Graph Embedding in Dissimilarity Space
Graph edit distance d(g 1 ,g 2 ) • Measures the distance (dissimilarity) of given graphs g 1 and g 2 • Is based in the idea of editing g 1 into g 2 • Common edit operations are deletion, insertion and substitution of nodes and edges • Can be used with a cost function • Is computationally expensive, but approximate solutions with complexity O(n 3 ) exist
Graph Embedding by 1st and 2nd Order Node Label Statistics φ (g )=(2,4,0,1,0,2,0,0,0,0,4,0,0,0) nodes edges • Equivalent to counting the number of nodes with a certain label, and the number of edges between pairs of nodes with given labels • Only O(n)+O(e) time complexity • Extensions: Continuous (non-discrete) node labels Edges labels Experimental results comparable with dissimilarity space embedding
Application 1: Automatic Transcription of Handwritten Medieval Text A. Fischer. Handwriting Recognition and Historical Documents. Phd Thesis, University of Bern, 2012 • Digitization of historical documents has become a focus of intensive research • Objective is to maintain cultural heritage and make vast amounts of historical material available on the internet • Not only digitization, but also transcription is needed
Challenges in the Transcription of Handwritten Historical Documents • Layout analysis and extraction of text – Decorations – Decay of paper or parchment – Faded ink – Bleed through – Various other artifacts • Acquisition of training samples for recognition costly and difficult (language often known only to experts, special letters) • Lack of language model, etc.
Conventional Approach
Conventional Features • Based on a sliding window, e.g. features by – Marti et al.: 9 features extracted from a window of 1 pixel width – Vinciarelli et al.: 16 windows of size 4 x 4 pixel; fraction of black pixels in each window; result: 16 features
• Potential problem with conventional approach: – Two-dimensional shape of characters is not adequately modeled; no structural relations • Possible solution: – Use skeletons to represent the handwriting by a graph – Transform the graph of a handwritten text into a sequence of feature vectors – Apply HMMs or RNN to sequence of feature vectors
Graph Extraction • Apply a thinning operator to generate the skeleton of the image • Nodes: – Key points: crossings, junctions, end points, left-most points of circular arcs – Secondary points: equidistant points on the skeleton between key points; distance d is a parameter • Edges: – Nodes that are neighbors on the skeleton are connected by edges – However, in the experiments it turned out that the performance without edges is comparable to that with edges if parameter d is chosen appropriately; therefore, no edges were used
General Idea of Graph Based Approach
Prototype Selection • One prototype per class manually selected • Prototypes automatically selected from automatically extracted characters Sliding Window • Width of window is dynamically adapted to width of prototype
Experimental Results
Selected Prototypes • Number of prototypes for Spanning and k-Centers was determined from the interval [1,5] on a validation set
Comments • In this application, graph-matching based feature extraction could reduce the error rate by about 50% compared to a standard set of features • Because the graphs are rather small, the additional computational cost is moderate (compared to HMM decoding) • Combining different feature sets or different classifiers with each other could be an interesting topic for further studie s • Recent experiments with alternative graph distance measures have given promising results
Application 2: Brain State Decoding Using Functional Magnetic Resonance Imaging (fMRI) J. Richiardi, D. Van De Ville, K. Riesen, and H. Bunke. Vector space embedding of undirected graphs with fixed-cardinality vertex sequences for classification. In Proc. 20th Int. Conference on Pattern Recognition, pages 902 – 905. IEEE Computer Society Press, 2010. J. Richiardi, S. Achard, H. Bunke, D. Van De Ville, D.: Machine learning with brain graphs, IEEE Signal Processing Magazine, 2013 to appear • Partners: University of Geneva, EPFL Lausanne, University of Bern • Task: from fMRI data, decide whether a person is resting or watching a movie • Perspective in the long range: – “Mind reading” – Better understanding of the brain – Clinical use (better diagnostic and therapeutic procedures)
fMRI is a technique for measuring brain activity. It works by detecting the changes in blood oxygenation and flow that occur in response to neural activity. When a brain area is more active it consumes more oxygen and to meet this increased demand blood flow increases to the active area. Hence, fMRI can be used to produce activation maps showing which parts of the brain are involved in a particular mental process.
Basic model/understanding in this work: brain is a graph
Data Acquisition • fMRI images from 15 subjects (4-D data) • Spatio-temporal resolution 3.75 x 3.75 x 4.2 mm 3 x 1.1 s • 9 alternating blocks of resting (90 s) and watching movie (50s), concatenated to one sequence for each activity • All voxels are mapped to a brain atlas that contains 90 regions • As a result, one gets two time sequence x 1 ,x 2 ,…, x n and y 1 ,y 2 ,…, y m for each region, one for each activity • These time series are filtered into four sub-bands using orthogonal discrete wavelet transform • Finally, four times series are obtained for each region and each activity
Graph Generation • Nodes: each region of the brain atlas is represented by a node; for each node we have four times series (for each of the two activities) • Edges: the graph is completely connected and has weighted edges; the edge weight is the correlation coefficient r ∊ [-1,1] between two time series of the same sub-band and the same activity
Classification Experiment • Graphs were transformed to features vectors (graph embedding) – Concatenate upper right diagonal of adjacency matrix into one long vector (d=4005) – Apply dissimilarity space embedding, using all graphs from the training set as prototypes (d=29) • Three standard classifiers were applied (all from WEKA): – SVM with linear kernel – Decision forest – Multilayer perceptron (only for dissimilarity space embedding) • Leave-one-out protocol because of small data set (15 graphs per class and subband)
Experimental Results
Comments • Direct embedding yields feature vectors of very high dimensionality • Dissimilarity space embedding yields feature vectors of rather low dimensionality (due to small data set) • A solution in between could lead to even better results – Apply feature reduction methods after direct embedding – Extend data set to obtain more prototypes (i.e. dimensions) for dissimilarity embedding • A combination of several, or all, sub-bands could be beneficial as well
Summary, Discussion, and Conclusions • Structural PR allows us to represent objects in terms of their parts and relations between them, which is an advantage over statistical PR • On the other hand, statistical PR offers a wealth of mathematical tools for classification, clustering, and similar tasks • Graph kernels and graph embedding allow us to get the best from both worlds • In addition to introducing graph kernels and graph embedding in this talk, we have reviewed two applications where these concepts were successfully applied • There remain a number of challenges for future research: – Make methods faster (like linear time embedding) – Make them able to deal with graphs consisting of millions of nodes – Develop software tools and make them available on the web
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